The Modular Group, Operator Ordering, and Time in (2+1)-Dimensional Gravity

Details The Modular Group, Operator Ordering, and Time in (2+1)-Dimensional Gravity The Modular Group, Operator Ordering, and Time in (2+1)-Dimensional Gravity

1992-09-25

arxiv.org/abs/gr-qc/9209011v1

Phys.Rev.D47:4520-4524,1993

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, LaTeX

Scientific paper

10.1103/PhysRevD.47.4520

A choice of time-slicing in classical general relativity permits the construction of time-dependent wave functions in the ``frozen time'' Chern-Simons formulation of $(2+1)$-dimensional quantum gravity. Because of operator ordering ambiguities, however, these wave functions are not unique. It is shown that when space has the topology of a torus, suitable operator orderings give rise to wave functions that transform under the modular group as automorphic functions of arbitrary weights, with dynamics determined by the corresponding Maass Laplacians on moduli space.

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